Measurement Error Problems Research Articles

Peter Hall’s main contributions to deconvolution

Peter Hall died in Melbourne on January 9, 2016. He was an extremely prolific researcher and contributed to many different areas of statistics. In this paper, I talk about my experience with Peter and I summarise his main contributions to deconvolution, which include measurement error problems and problems in image analysis.

Estimating Intergenerational Mobility With Grouped Data

This article distinguishes three measures of intergenerational economic mobility that emerge when the population is divided into groups: overall individual mobility, within-group mobility, and between-group mobility. We clarify their properties and the relationship between them. We then evaluate Clark’s use of surname between-group persistence as a preferred measure of intergenerational mobility in the book The Son Also Rises: Surnames and the History of Social Mobility. We show that aggregate surname-level intergenerational persistence cannot be compared with individual persistence because group-level income averages captures diverse individual-level and group-level factors impossible to disentangle without additional identifying information. Furthermore, measures of group persistence do not address the problem of measurement error leading to attenuation bias, which is Clark’s rationale to study surname mobility. An empirical example partitioning the population into groups based on racial/ethnic origins and a simulation clarify the relationship between these different measures of mobility.

Moment reconstruction and moment-adjusted imputation when exposure is generated by a complex, nonlinear random effects modeling process.

For the classical, homoscedastic measurement error model, moment reconstruction (Freedman etal., 2004, 2008) and moment-adjusted imputation (Thomas etal., 2011) are appealing, computationally simple imputation-like methods for general model fitting. Like classical regression calibration, the idea is to replace the unobserved variable subject to measurement error with a proxy that can be used in a variety of analyses. Moment reconstruction and moment-adjusted imputation differ from regression calibration in that they attempt to match multiple features of the latent variable, and also to match some of the latent variable's relationships with the response and additional covariates. In this note, we consider a problem where true exposure is generated by a complex, nonlinear random effects modeling process, and develop analogues of moment reconstruction and moment-adjusted imputation for this case. This general model includes classical measurement errors, Berkson measurement errors, mixtures of Berkson and classical errors and problems that are not measurement error problems, but also cases where the data-generating process for true exposure is a complex, nonlinear random effects modeling process. The methods are illustrated using the National Institutes of Health-AARP Diet and Health Study where the latent variable is a dietary pattern score called the Healthy Eating Index-2005. We also show how our general model includes methods used in radiation epidemiology as a special case. Simulations are used to illustrate the methods.

Deferred Judgment in Foreign Policy Opinion: The Impact of Cost Procrastination on Audience Costs

The Obama administration’s 2013 policy crisis concerning intervention in the Syrian civil war features the domestic audience acting opposite our most pivotal theoretical predictions. Initial polls showed support for intervention, but the audience resisted Obama’s efforts to follow through on his threat, forcing him to change course and back down. This contradicts the audience cost proposal that citizens prefer consistency by leaders. The reversal can be explained by measurement error in early polls. I argue that survey experiments on audience preferences, which lack information on context and cost, have measurement error problems as bad as or worse than polls on opinion in real crises. I push for revamped tests that account for the types of response error studied in psychology and economics. Security scholars should try to put experimental subjects in the same frame of mind they are in when making decisions about their political opinions. I provide experimental evidence for the need to start adjusting for these measurement problems, and I propose an agenda for making inferential improvements to experimental studies of public opinion on international conflict.

Improving Efficiency Using the Rao–Blackwell Theorem in Corrected and Conditional Score Estimation Methods for Joint Models

Longitudinal covariates in survival models are generally analyzed using random effects models. By framing the estimation of these survival models as a functional measurement error problem, semiparametric approaches such as the conditional score or the corrected score can be applied to find consistent estimators for survival model parameters without distributional assumptions on the random effects. However, in order to satisfy the standard assumptions of a survival model, the semiparametric methods in the literature only use covariate data before each event time. This suggests that these methods may make inefficient use of the longitudinal data. We propose an extension of these approaches that follows a generalization of Rao-Blackwell theorem. A Monte Carlo error augmentation procedure is developed to utilize the entirety of longitudinal information available. The efficiency improvement of the proposed semiparametric approach is confirmed theoretically and demonstrated in a simulation study. A real data set is analyzed as an illustration of a practical application.

Impact of Ex‐Ante Hypothetical Bias Mitigation Methods on Attribute Non‐Attendance in Choice Experiments

AbstractIn this article, we use survey data from Nigeria on consumers' preferences for organic products to investigate the impact of ex‐ante hypothetical bias mitigation methods (Cheap Talk and Honesty Priming) on respondents' attribute non‐attendance. We employ a framework that allows us to jointly examine the response to the stated choice component and the response to the attribute processing questions, while avoiding the potential endogeneity bias and measurement error problems arising from some attribute non‐attendance methods. Our results show that the incidence of attribute non‐attendance varies across the treatments in general, with significant difference in attribute non‐attendance rates between respondents exposed to the mitigation strategies (Honesty Priming and Cheap Talk) and the baseline group. We also find that the low willingness to pay values for the honesty priming task appear to correspond with the lowest attribute non‐attendance rates reported for all the attributes (especially price) and might reflect a more realistic valuation of the attributes.

Error-Compensation Method for Inclination Measurement Under the Influence of the Dynamic Interference

To deal with the problem of the inclination measurement errors caused by the dynamic motions, such as rotational and accelerated rectilinear components, this paper puts forward an effective inclination measurement scheme and the corresponding error-compensation method based on one accelerometer and two gyroscopes. In addition, the principle prototype of the dynamic inclination measurement apparatus is set up to conduct experiments of turntable rotation test, trolley test, and the turntable sway test at different inclined angles, thus verifying the feasibility of the error-compensation method under the effects of the rotational motion, accelerated rectilinear motion or both motions at the same time. Experimental results show that the aforementioned method can effectively compensate the inclination measurement errors resulting from the rotational and accelerated rectilinear motions.

ORDINAL VERSIONS OF V-DEM’S INDICES: WHEN INTERVAL MEASURES ARE NOT USEFUL FOR CLASSIFICATION, DESCRIPTION, AND SEQUENCING ANALYSIS PURPOSES

In the wake of the Cold War democracy has gained the status of a mantra.1 However, no consensus has emerged about how to conceptualize and measure this key concept. For policymakers, activists, academics, and citizens around the wor ld the conceptualization and measurement of democracy matters. Billions of dollars in foreign aid spent every year for promoting democracy and governance in the developing world are contingent upon judgments about a polity's current status, its recent history, future prospects, and the likely causal effect of particular forms of assistance. A large body of social science work deals with these same issues. The needs of democracy promoters and social scientists are convergent. We all need better ways to measure democracy.The study of democracy and democratization lies at the center of political science and is increasingly important in economics, sociology, and history. In the post-Cold War world, democracy has also become a central foreign policy objective for many countries, and is often a critical condition for the distribution of international development assistance. The transition to democracy and its consolidation remain key issues in global development today. Yet, uncertainty persists over why some countries become and remain democratic and others do not (e.g. Acemoglu and Robinson 2006, Boix 2003, Houle 2009, Inglehart et al. 2005, Lindberg 2009, Lipset 1959, Paxton 2000, Przeworski et al. 2000, Teorell 2010). The recent literature provides a range of specific hypotheses that, while accompanied by relatively sophisticated empirical strategies for testing, reach few firm conclusions.One of the obstacles to advancement in the field of democratization studies is the absence of a wide-ranging database that tracks multifarious aspects of countries' institutional histories. Several democracy-measurement ventures cover only democracies (e.g. Lijphart 1999) or particular regions (e.g. Munck 2009, Lindberg 2006), or just one aspect such as elections (e.g. NELDA). Existing democra cy indic es that seek to measur e democr a cy tend to be problematic in several respects. This includes the BNR index developed by Bernhard, Nordstrom & Reenock (2001); the Bertelsmann Transformation Index (BTI) directed by the Bertelsmann Stiftung (various years); the Democracy Barometer developed by Wolfgang Merkel & associates (Buhlmann, Merkel, Muller & Wesels 2012); the BMR index developed by Boix, Miller & Rosato (2013), the Contestation and Inclusiveness indices developed by Coppedge, Alvarez, & Maldonado (2008); the Political Rights, Civil Liberty, Nations in Transit, and Countries at the Crossroads indices, all sponsored by Freedom House (freedomhouse.org); the Economist Intelligence Unit (2010) index ( EIU); t he Unif i ed Democracy Scor es (UDS) developed by Pemstein, Meserve, & Melton (2010); the Polity2 index from the Polity IV database (Marshall, Gurr, & Jaggers 2014); the democracy-dictatorship (DD) index develop ed by Ada m Przeworski & collea gues (Alva r ez, C heibub, Limongi, & Przeworski 1996; Cheibub, Gandhi, & Vr eela nd 2010); t he Lexical index of democracy developed by Skaaning, Gerring, & Bartusevicius (2015); the Competition and Participation indices developed by Tatu Vanhanen (2000); and the Voice and Accountability index developed as part of the Worldwide Governance Indicators (WGI) (Kaufmann, Kraay, & Mastruzzi 2010).To summarize the issues with this range of alternatives broadly for the sake of brevity: i) they focus primarily on the electoral dimension of democracy; ii) they are comprised of components not measured independently of each other; iii) except for Polity IV, they do not extend back far in time for a global sample of countries; iv) they are not transparent in design and replicable, hence the accuracy of the data is either unknown or unreported; v) they do not address potential problems of measurement error and vi) they cannot make fine distinctions across polities or through time in a reliable fashion (Treier & Jacka mn 2008; P emst ein et al. …

Is natural experiment a cure? Re-examining the long-term health effects of China's 1959–1961 famine

The fetal origins hypothesis posits that adverse prenatal exposures, particularly malnutrition, increase the risk of poor adult health. Studies using famine as a natural experiment to test the fetal origins hypothesis present conflicting findings, partly because of data limitations and modeling flaws. Capitalizing on the biomarker data and prefecture-level geographic information from the 2011 China Health and Retirement Longitudinal Study, this study estimates the effects of prenatal exposure to China's 1959–61 famine on later-life risks of cardiovascular and metabolic diseases. Our analysis addresses the problems of measurement error and intrinsic cohort differences that challenge prior studies. We use provincial and prefecture-level geographic variations in famine severity, a proxy for prenatal malnutrition, for model identification. We construct instrumental variables from geocoded newspaper archive data to adjust for measurement error in famine exposure. We find that estimates of the famine effects are highly sensitive to the choices of health indicators, measures of famine severity, and regression model specifications. Overall, we find little evidence supporting the fetal origins hypothesis. In fact, it appears that prenatal exposure to famine reduces later-life disease risks in certain cases. We interpret this finding as evidence of mortality selection among the famine survivors at work. We conclude that using famine as a natural experiment in itself does not guarantee correct statistical inference about the long-term health impacts of prenatal malnutrition when other analytical challenges remain unresolved.

The Problem of Measurement Error in Self-Reported Receipt of Child-Care Subsidies: Evidence from Two States

AbstractResearchers frequently rely on survey responses to determine whether families receive government assistance and to study the effects of government programs, but these responses are often inaccurate. This study investigates misreporting in the child-care subsidy program by comparing survey responses on child-care subsidy receipt with program administrative data in two states. While we find a lower rate of misreporting than is typical for other government assistance programs, overreporting of benefit receipt is surprisingly common and generates overestimates of program participation. Analyses further suggest that the frequency and systematic nature of misreporting bias estimates of the predictors of program receipt and the effects of the program. These findings illustrate the necessity of assessing the frequency of response errors and understanding their implications in generating valid research results on the effects of government programs.

Statistical power as a function of Cronbach alpha of instrument questionnaire items.

BackgroundIn countless number of clinical trials, measurements of outcomes rely on instrument questionnaire items which however often suffer measurement error problems which in turn affect statistical power of study designs. The Cronbach alpha or coefficient alpha, here denoted by Cα, can be used as a measure of internal consistency of parallel instrument items that are developed to measure a target unidimensional outcome construct. Scale score for the target construct is often represented by the sum of the item scores. However, power functions based on Cα have been lacking for various study designs.MethodsWe formulate a statistical model for parallel items to derive power functions as a function of Cα under several study designs. To this end, we assume fixed true score variance assumption as opposed to usual fixed total variance assumption. That assumption is critical and practically relevant to show that smaller measurement errors are inversely associated with higher inter-item correlations, and thus that greater Cα is associated with greater statistical power. We compare the derived theoretical statistical power with empirical power obtained through Monte Carlo simulations for the following comparisons: one-sample comparison of pre- and post-treatment mean differences, two-sample comparison of pre-post mean differences between groups, and two-sample comparison of mean differences between groups.ResultsIt is shown that Cα is the same as a test-retest correlation of the scale scores of parallel items, which enables testing significance of Cα. Closed-form power functions and samples size determination formulas are derived in terms of Cα, for all of the aforementioned comparisons. Power functions are shown to be an increasing function of Cα, regardless of comparison of interest. The derived power functions are well validated by simulation studies that show that the magnitudes of theoretical power are virtually identical to those of the empirical power.ConclusionRegardless of research designs or settings, in order to increase statistical power, development and use of instruments with greater Cα, or equivalently with greater inter-item correlations, is crucial for trials that intend to use questionnaire items for measuring research outcomes.DiscussionFurther development of the power functions for binary or ordinal item scores and under more general item correlation strutures reflecting more real world situations would be a valuable future study.

Consequences of Measurement Error for Inference in Cross-Lagged Panel Design—The Example of the Reciprocal Causal Relationship Between Subjective Health and Socio-Economic Status

We discuss the problem of random measurement error in two variables when using a cross-lagged panel design. We apply the problem to the question of the causal direction between socio-economic status and subjective health, known also as health selection versus social causation. We plot the bias of the ratio between the social causation and the health selection coefficient as a function of the degree of measurement error in subjective health and socio-economic status for different scenarios which might occur in practice. Using simulated data we give an example of a Bayesian model for the treatment of measurement error that relies on external information about the degree of measurement error.

First‐time House Buying and Catch‐up: A Cohort Study

We investigate whether different ages of first‐time house buying lead to persistent differences in homeownership between cohorts. Our data span nearly 40 years and multiple cycles of England's volatile house prices. Ownership rates at thirty have differed substantially, with a significant negative association with prices. The persistence of differences is assessed using synthetic cohort techniques. Two methods of dealing with measurement error problems both indicate that cohorts with low ownership rates at thirty catch up almost all of the ownership gap by forty. Earlier access to homeownership may result in the ownership of slightly larger homes at around forty.

A New Method to Measure the Output Torque for Micromotor

A noncontact measuring method has been proposed to measure the micronewton meter-order output microtorque of micromotors to overcome the problem of large measurement errors caused by temperature, vibration, friction, and the flow of air. Physical model of this method is built according to Newton’s third law and the electromagnetic theory. To realize this method, an apparatus named noncontact microtorque measuring equipment is designed to measure the output torque of micronewton meter-order micromotors. This device is mainly composed of electromagnetic windings, control circuit, an electronic balance, and a photoelectric sensor. Working principle of this device is introduced and the measured precisions of rotating speed and microtorque of the device are also analyzed in detail. Finally, a microelectromechanical system fabricated planar dc micromotor is tested by this device. The analyzed precision of the microtorque is 0.01 $\mu \text{N}\,{\cdot }\,\text{m}$ , which is precise enough for the measurement. The tested result indicates this method is feasible to measure the micronewton meter-order output microtorque of the micromotor.

Does rice farming shape individualism and innovation?

Talhelm et al. (2014) provided an original rice theory to explain large psychological differences across countries and even within countries and their impact on innovation. However, their findings are subject to the problems of sample bias, measurement error, and model misspecification. After correcting these problems, most findings in the original paper no longer hold. We collected data on collectivism from other sources and linked them with rice areas but failed to find any relationship as predicted by the rice theory. The role of rice farming in shaping cultural psychology and innovations seems to be much more muted than asserted in Talhelm et al. (2014).

A statistical model for measurement error that incorporates variation over time in the target measure, with application to nutritional epidemiology.

Most statistical methods that adjust analyses for measurement error assume that the target exposure T is a fixed quantity for each individual. However, in many applications, the value of T for an individual varies with time. We develop a model that accounts for such variation, describing the model within the framework of a meta-analysis of validation studies of dietary self-report instruments, where the reference instruments are biomarkers. We demonstrate that in this application, the estimates of the attenuation factor and correlation with true intake, key parameters quantifying the accuracy of the self-report instrument, are sometimes substantially modified under the time-varying exposure model compared with estimates obtained under a traditional fixed-exposure model. We conclude that accounting for the time element in measurement error problems is potentially important.

Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems.

In truncated polynomial spline or B-spline models where the covariates are measured with error, a fully Bayesian approach to model fitting requires the covariates and model parameters to be sampled at every Markov chain Monte Carlo iteration. Sampling the unobserved covariates poses a major computational problem and usually Gibbs sampling is not possible. This forces the practitioner to use a Metropolis-Hastings step which might suffer from unacceptable performance due to poor mixing and might require careful tuning. In this article we show for the cases of truncated polynomial spline or B-spline models of degree equal to one, the complete conditional distribution of the covariates measured with error is available explicitly as a mixture of double-truncated normals, thereby enabling a Gibbs sampling scheme. We demonstrate via a simulation study that our technique performs favorably in terms of computational efficiency and statistical performance. Our results indicate up to 62 and 54 % increase in mean integrated squared error efficiency when compared to existing alternatives while using truncated polynomial splines and B-splines respectively. Furthermore, there is evidence that the gain in efficiency increases with the measurement error variance, indicating the proposed method is a particularly valuable tool for challenging applications that present high measurement error. We conclude with a demonstration on a nutritional epidemiology data set from the NIH-AARP study and by pointing out some possible extensions of the current work.

Endogenous Markov Switching Regression Models for High-Frequency Data Under Microstructure Noise

We present a novel method in analyzing microstructure noise of high-frequency data as a measurement error problem within an endogenous Markov-switching regression model. In this model, the regression disturbance and the latent state variable controlling the regime are correlated. We show that under endogeneity the popular realized variance estimator is biased and no longer converges to the integrated regime dependent volatility. Exploring intraday return data on foreign exchange rates, we find significant endogeneity at high frequencies. Similar to the popular volatility signature plot suggested by Andersen, Bollerslev, Diebold, and Labys (2000b), we propose an endogeneity plot, which indicates as to which sampling frequency the assumption of exogeneity of the state variable controlling the regime remains valid.

The Extensively Corrected Score for Measurement Error Models

AbstractIn measurement error problems, two major and consistent estimation methods are the conditional score and the corrected score. They are functional methods that require no parametric assumptions on mismeasured covariates. The conditional score requires that a suitable sufficient statistic for the mismeasured covariate can be found, while the corrected score requires that the object score function can be estimated without bias. These assumptions limit their ranges of applications. The extensively corrected score proposed here is an extension of the corrected score. It yields consistent estimations in many cases when neither the conditional score nor the corrected score is feasible. We demonstrate its constructions in generalized linear models and the Cox proportional hazards model, assess its performances by simulation studies and illustrate its implementations by two real examples.

Unemployment matters: Improved measures of labor market distress in mortgage default analysis

An outstanding feature in cities is the spatial relationship between housing and labor markets. The spatial relationship occurs because a worker's workplace is spatially separated from his/her residence. This separation imposes a geographic barrier to better understanding the interactions between housing and labor markets, especially at a micro level. Overlooking this spatial interdependency of workplace and residential locations in the existing empirical studies may explain their inconclusive or mixed results for job loss effect on foreclosure. Our paper develops a job loss vulnerability index to overcome this geographic barrier by using pair-wise home-work commute data between census tracts. After controlling for the endogeneity and measurement error problems, we find that job loss plays an important role in foreclosure decisions, particularly with rising negative equity. More specifically, estimated results suggest that when house prices drop by 10%, 30% and 50%, doubling job loss would increase foreclosure rate by about 15%–25%, 40%–60%, and 60%–100%, respectively. Estimate results are consistent and robust with different data, different estimators, and different measures of variables.